NTA JEE Main 25th February 2021 Shift 1
For the following questions answer them individually
NTA JEE Main 25th February 2021 Shift 1 - Question 61
The integer $$k$$, for which the inequality $$x^2 - 2(3k - 1)x + 8k^2 - 7 > 0$$ is valid for every $$x$$ in $$R$$ is:
NTA JEE Main 25th February 2021 Shift 1 - Question 62
Let the lines $$(2 - i)z = (2 + i)\bar{z}$$ and $$(2 + i)z + (i - 2)\bar{z} - 4i = 0$$, (here $$i^2 = -1$$) be normal to a circle $$C$$. If the line $$iz + \bar{z} + 1 + i = 0$$ is tangent to this circle $$C$$, then its radius is:
NTA JEE Main 25th February 2021 Shift 1 - Question 63
The total number of positive integral solutions $$(x, y, z)$$ such that $$xyz = 24$$ is:
NTA JEE Main 25th February 2021 Shift 1 - Question 64
If $$0 < \theta, \phi < \frac{\pi}{2}$$, $$x = \sum_{n=0}^{\infty} \cos^{2n}\theta$$, $$y = \sum_{n=0}^{\infty} \sin^{2n}\phi$$ and $$z = \sum_{n=0}^{\infty} \cos^{2n}\theta \cdot \sin^{2n}\phi$$ then:
NTA JEE Main 25th February 2021 Shift 1 - Question 65
All possible values of $$\theta \in [0, 2\pi]$$ for which $$\sin 2\theta + \tan 2\theta > 0$$ lie in:
NTA JEE Main 25th February 2021 Shift 1 - Question 66
The image of the point (3, 5) in the line $$x - y + 1 = 0$$, lies on:
NTA JEE Main 25th February 2021 Shift 1 - Question 67
A tangent is drawn to the parabola $$y^2 = 6x$$ which is perpendicular to the line $$2x + y = 1$$. Which of the following points does NOT lie on it?
NTA JEE Main 25th February 2021 Shift 1 - Question 68
If the curves, $$\frac{x^2}{a} + \frac{y^2}{b} = 1$$ and $$\frac{x^2}{c} + \frac{y^2}{d} = 1$$ intersect each other at an angle of 90°, then which of the following relations is TRUE?
NTA JEE Main 25th February 2021 Shift 1 - Question 69
$$\lim_{n \to \infty} \left(1 + \frac{1 + \frac{1}{2} + \ldots + \frac{1}{n}}{n^2}\right)^n$$ is equal to
NTA JEE Main 25th February 2021 Shift 1 - Question 70
The statement $$A \to (B \to A)$$ is equivalent to:
